For these two sequences exact results are not available, but both belong to a set of HP
sequences that have been widely used to test novel (classical) algorithms [1]}.
The lowest known energies are \(E_{\text{HP}}=-23\)  for S\(_{48}\)  [2]}
and \(E_{\text{HP}}=-42\)  for S\(_{64}\)  [3]}. We performed hybrid computations for
both sequences on a \(10^2\)  grid. In order to obtain good results, the \(\lambda _i\)  parameters
had to be adjusted. For S\(_{48}\) , the lowest known energy, \(E_{\text{HP}}=-23\) , was recovered in 10
of 100 hybrid runs, using \({\lambda }=(2.0,3.5,3.0)\) . For S\(_{64}\) , with \({\lambda }=(3.0,4.0,4.0)\) ,
a structure with the lowest known energy, \(E_{\text{HP}}=-42\) , was obtained in 1 of 200 hybrid runs. This
folded structure is depicted in Fig. REF .
<FIGURE>